As a conventional double-ringed fluorescent lamp, there is known, for example, as shown in FIG. 21, a double-circular fluorescent lamp 321. In such a double-circular fluorescent lamp 321, there is provided, on the outer side of an inner ring glass bulb 322 having ring shape, an outer ring glass bulb having a ring shape and a larger diameter than the inner ring glass bulb so as to be placed concentrically on the same plane. A connection portion 324 connects respective discharge paths of the inner and outer ring glass bulbs 322, 323 to each other to form a single discharge path so that an increased length of the discharge path can enhance the total luminous flux and the luminous efficiency (as disclosed, for example, following Patent Document 1).
Such a kind of fluorescent lamp has an increased length of the discharge path in comparison with the other lamp, which is composed of a single ring bulb, thus enhancing the total luminous flux and the luminous efficiency.
Patent Document 1: Japanese Patent Laid-open (KOKAI) Publication No. HEI 9-129180.
However, in a manufacturing process of the conventional double-circular fluorescent lamp 321 disclosed in the above Patent Document 1, a protection layer and a phosphor layer are formed on inner surfaces of two straight tubular glass bulbs 322, 323, and then these bulbs are heated to be softened and wound around cylindrical drums so as to be bent into a ring shape. Accordingly, there is a problem that fissure, flaking off or crack may easily occur on the protection layer or the phosphor layer.
After completion of the ring-shape bending process for the ring glass bulbs 322, 323, the connection portion 324 is formed. However, it is not always easy to carry out the formation process of the connection portion 324, and the strength of the connection portion 324 is apt to be deteriorated, thus causing problems. More specifically, the inner and outer ring glass bulbs 322, 323 are heated so as to be softened in their entirety and subjected to the bending process. Then, flame from a burner is blown onto portions of these bulbs, on which the connection portion 324 is to be formed, to heat them locally to soften, and at this time, gas is blasted into the glass bulbs 322, 323 so that bulb walls thereof project outward under the function of the gas pressure and are broken by blast to form apertures thereon. Then, the blast-broken ends of these portions as projected outward are connected to each other by fusion (i.e., the burner blast breaking) so that these apertures communicate with each other to form the connection portion 324.
The heating process through the burner blast breaking is carried out to blow the flame from the burner onto the portions of the inner and outer ring glass bulbs 322, 323, on which the connection portion is to be formed, to heat them to soften, in a state that residual strain caused by the heating in the bending process still exists on the glass bulbs 322, 323 in their entirety. As a result, damage such as crack may easily occur on the connection portion 324 or in the vicinity thereof. The glass bulbs 322, 323 are provided on their respective ends with groove portions “m” formed thereon, which are utilized to carry out the bending process. The connection portion 324 cannot be formed in the vicinity of the groove portion “m” and must be formed apart from the end of the bulb. This leads to a decreased length of the discharge paths of the bulbs 322, 323, thus deteriorating the luminous efficiency.
In addition, the burner blast breaking process must be carried out to couple partially a convexly arched outer surface of the inner ring glass bulb 322 and a concavely arched inner surface of the outer ring glass bulb 323 to each other in a narrow gap (for example, of from 1 mm to 3 mm) between the inner and outer ring glass bulbs 322, 323, so as to form the connecting portion 324, as shown in FIG. 22. Therefore, it is not easy to carry out the coupling operation due to difference in radius of curvature between the opposing circumferential surfaces of the bulbs, thus causing problems.
Each of the inner and outer ring glass bulbs 322, 323 is formed into a ring shape as shown in FIGS. 21 and 22, and there is formed a space having a trapezoidal shape between the outer end surfaces 327a, 328a, in the axial direction of the tube, of electrode-sealed end portions 327, 328 by which a pair of electrodes 325, 326 are sealed, respectively, and the opposing outer end surfaces 329a, 330a on the side of the connecting portion 324 in the circumferential direction so that the distance “La” between the end surfaces 327a and 329a is smaller than the distance “Lb” between the end surfaces 328a and 330a. 
The increased distances “La”, “Lb” on the side of the outer peripheral surfaces in such a trapezoidal space results in the decreased length of the discharge path of the whole fluorescent lamp 21. Accordingly, a non-luminous or dark area is increased, a base 331, which is mounted between the electrode-sealed end portions 327, 328 and the opposing ends on the side of the connecting portion 324 so as to cover them, is formed into a fan shape and has a large size, thus causing problems.